Bounded solutions of linear periodic abstract parabolic equations

Source abstract

Synopsis We study the asymptotic behaviour of the parabolic evolution operator G ( t , s ) associated with a family of generators of analytic semigroups { A ( t ); t ∊ ℝ} in general Banach space, under the periodicity assumption A ( t ) = A ( t + T ). We find new maximal regularity results for the bounded solutions of abstract nonhomogeneous parabolic equations in unbounded time intervals.